Lowercase or capital letter after a colon? Depends. When it’s used within a sentence, the first word following the colon is lowercased unless it’s a proper name.
There are two kinds of people: those who generalize and those who don’t.
When a colon introduces two or more sentences, however—or when it introduces speech in dialogue—the first word following it is capitalized.
CK was faced with an impossible choice: Should he complete his evening ensemble with the charcoal jacket in hand-finished merino wool? Or should he throw caution to the wind and wear the grey pinstripe with Jacquard stitching?